DescriptionSoft errors are increasing in modern computer systems. These faults can corrupt the results of numerical solvers commonly used in scientific and electromagnetic simulations. If the severity of a bitflip is high, then our numerical code might never converge. There are several techniques to address the issue of soft faults in numerical solvers. Self-stabilizing and Algorithm-Based Fault Tolerance (ABFT) techniques are notably the most popular choice when it comes to designing a fault tolerant scheme. Selfstabilizing numerical methods have been developed to retrieve numerical stability in the presence of faults at the cost of running computation-intensive reliable iterations. Our work presents efficient techniques to determine when to execute the correction loop in Self-stabilizing conjugate gradient methods (SS-CG). The proposed adaptive-F and invariant check strategies have low overheads compared to current techniques used in self-stabilizing methods. Developing resiliency in the presence of multiple faults is another challenging aspect of fault tolerance. Most researchers consider the effect of a single bitflip while designing their fault tolerant schemes. In this thesis, we address the importance of addressing multiple faults and propose a novel recursive block checkSum strategy to localize errors and correct them in sparse numerical code.